Information on Result #1304208
Linear OA(369, 277, F3, 19) (dual of [277, 208, 20]-code), using 12 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 5 times 0) based on linear OA(365, 261, F3, 19) (dual of [261, 196, 20]-code), using
- construction XX applied to C1 = C([239,13]), C2 = C([0,15]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([239,15]) [i] based on
- linear OA(356, 242, F3, 17) (dual of [242, 186, 18]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,13}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(351, 242, F3, 16) (dual of [242, 191, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(361, 242, F3, 19) (dual of [242, 181, 20]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,15}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(346, 242, F3, 14) (dual of [242, 196, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(369, 277, F3, 2, 19) (dual of [(277, 2), 485, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(369, 277, F3, 3, 19) (dual of [(277, 3), 762, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(369, 277, F3, 4, 19) (dual of [(277, 4), 1039, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(369, 277, F3, 5, 19) (dual of [(277, 5), 1316, 20]-NRT-code) | [i] | ||
| 5 | Digital (50, 69, 277)-net over F3 | [i] | ||